The paper concerns a Dirichlet problem for the equation - A.u + F(x,y,u,ux,Uy) = 0'on a rectangle. An iteration process for solving a nonlinear system of algebraic equations which arise in collocation method is considered. A convergence and an error estimate are obtained. Numerical results are presented for equations with F=cu+eu+f(x,y).
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In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a modified quasi-boundary value method to construct approximate stable solutions for the original ill-posed boundary value problem. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution. Moreover, numerical tests are presented to illustrate the accuracy and efficiency of this method.
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